Schema Equivalence and Optimization

Transcription

1 Reference: Mustafa Jarrar: Lecture Notes on Schema Equivalence and Optimization in ORM Birzeit University, Palestine, 2015 Schema Equivalence and Optimization Dr. Mustafa Jarrar University of Birzeit 1

2 Watch this lecture and download the slides Course Page: More Online Courses at: Some diagrams in this lecture are based on [1] Keywords: Schema, Schema Engineering, constraints, Schema Equivalence, Schema Optimization, constraints, Cardinality, multiplicity, Rules, Business Rules, Business logic derivation rules, integrity constraints 2

3 Conceptual Schema Design Steps 1. From examples to elementary facts 2. Draw fact types and apply population check 3. Combine entity types 4. Add uniqueness constraints 5. Add mandatory constraints 6. Add subtype relations and other constraints 7. Final checks, & schema engineering issues 3

4 Schema Equivalence and Optimization It is not surprising that people often come up with different ways (i.e., different conceptual models) of describing the same reality. Two conceptual schemas are equivalent if and only if whatever UoD state can be modeled in one can also be modeled in the other. What is the difference between these two schemes: ØThe act of reshaping two equivalent schemes like this is said to be a conceptual schema transformation. 4

5 Schema Equivalence and Optimization Skills of schema transformations helps you to see what different design choices are possible. Moreover, if two independently developed schemas are to be either fully or partly integrated, we often need to resolve the differences in the ways that each schema models common UoD features. To do this, we need to know whether one representation can be transformed into the other, and if so, how. Another use of conceptual schema transformations is to reshape the original conceptual schema into one that maps directly to a more efficient implementation, or to more conceptually elegant schema. This process is known as conceptual schema optimization. èthere are two class of schema transformations: Predicate Specialization, and Predicate Generalization 5

6 Predicate Specialization and Generalization If two or more predicates may be thought of as special cases of a more general predicate, then we may replace them by the more general predicate, so long as the original distinction can be preserved in some way. We generalize smoking and drinking into indulging in a vice, where vice has two specific cases. If we transform in the opposite direction, we specialize indulging in a vice into two predicates, one for each case. 6

7 Predicate Specialization and Generalization If two or more predicates may be thought of as special cases of a more general predicate, then we may replace them by the more general predicate, so long as the original distinction can be preserved in some way.? Because there are exactly three kinds of medals, the ternary may be specialized into three binaries, one for each medal kind, Where m³1, and each S i corresponds to R where B = b i Theory: R may be specialized into S 1..S n by absorbing B. 7

8 Predicate Specialization and Generalization The previous theorem always holds, but any constraint added to one of the schemas must be translated into an equivalent, additional constraint on the other schema. Each S i corresponds to R where B = b i The UC on the left is equivalent to the UCs on the right. Ø If a UC in R spans a combination of B s role and other roles, a UC spans the specialization of these other roles in S 1,..,S n, and conversely. 8

9 Predicate Specialization and Generalization? The UC on the left is equivalent to the exclusion constraint on the right.? The UC on the left is equivalent to the exclusion constraint on the right. Where m³1, and each S i corresponds to R where B = b i The UC on the left is equivalent to the exclusion constraint on the right. ØIf a UC spans all roles of R except for B s role, then S 1.. S n are mutually exclusive, and conversely. 9

10 Predicate Specialization and Generalization? if any medal results are recorded for a country, all three medal results (gold, silver, and bronze) are required. To express, we add an equality constraint between the medal winning roles played by Country. Ø If R is a ternary with a UC spanning just B s role and one other role, then adding a frequency constraint of n to this other role is equivalent to adding an equality constraint over the specialized versions of that role. 10

11 Predicate Specialization and Generalization The impact of adding mandatory role and frequency constraints.? Each S corresponds to R where B = b i Ø If A s role (or role disjunction) in R is mandatory, then the disjunction of its specialized roles is mandatory, and conversely (1 i m). Ø If R is a ternary with a UC spanning just B s role and one other role, then adding a mandatory role constraint and frequency constraint of n (the number of possible values for B) to this other role is equivalent to making each specialized version of that role mandatory. 11

12 Other Cases and Examples? Each car in the rally has two drivers (a main driver and a backup driver), and each person drives exactly one car. The drives predicate is specialized by absorbing Status. 12

13 Other Cases and Examples Each S i corresponds to R where T is restricted to B = b i Theory: R may be specialized into S 1..S n by absorbing B. Ø Corollary 1: If s roles are mandatory in the left-hand schema, the disjunction of s roles in the right-hand schema is mandatory, and conversely. Ø Corollary 2: If an external UC spans the roles of and in the left-hand schema, then a UC applies to each of s roles in the right-hand schema, and conversely. Ø Corollary 3: If s role in the left-hand schema is mandatory, then each of s roles in the right-hand schema is mandatory, and conversely. Ø Corollary 4: An equality constraint over s roles in the RHS is equivalent to a frequency constraint of on s role in the left-hand schema; this constraint is strengthened to if a UC exists on each of s roles in the right-hand schema. 13

14 Other Cases and Examples Can the predicate be specialized??? Transforming from the original schema to one of those strengthens the schema by adding information. Transforming in the opposite direction weakens the schema by losing information. ØAny such transformations that add or lose information should be the result of conscious decisions that are acceptable to the client (for which the business domain is being modeled). 14

15 Other Cases and Examples Each S i corresponds to one instance of R Theory: The left-hand schema implies the right-hand schema. Corollary 1:If an equality constraint applies over s roles in the left-hand schema, then the frequency constraint in the right-hand schema is strengthened to, and conversely. Corollary 2: Adding a UC to role in the right-hand schema is equivalent in the lefthand schema to adding UCs to s roles (making the S 1:1) and strengthening the exclusion constraint to an exclusion constraint over s roles. 15

16 References [1] Terry Halpin, Tony Morgan: Information Modeling and Relational Databases, Second Edition. Second Edition. The Morgan Kaufmann Series in Data Management Systems. ISBN: [2] Mustafa Jarrar and Robert Meersman: Ontology Engineering -The DOGMA Approach. Book Chapter in "Advances in Web Semantics I". Chapter 3. Pages LNCS 4891, Springer.ISBN: (2008). [3] Mustafa Jarrar, Anton Deik, Bilal Faraj: Ontology-Based Data And Process Governance Framework -The Case Of E-Government Interoperability In Palestine. In pre-proceedings of the IFIP International Symposium on Data-Driven Process Discovery and Analysis (SIMPDA 11). Pages(83-98). ISBN Campione, Italy. June 30, [4] Mustafa Jarrar: Mapping ORM Into The SHOIN/OWL Description Logic- Towards A Methodological And Expressive Graphical Notation For Ontology Engineering. In OTM 2007 workshops: Proceedings of the International Workshop on Object-Role Modeling (ORM'07). Pages ( ), LNCS 4805, Springer. ISBN: Portogal. November, 2007 [5] Mustafa Jarrar: Towards Automated Reasoning On ORM Schemes. -Mapping ORM Into The DLR_idf Description Logic. In proceedings of the 26th International Conference on Conceptual Modeling (ER 2007). Pages ( ). LNCS 4801, Springer. Auckland, New Zealand. ISBN November 2007 [6] Mustafa Jarrar and Stijn Heymans: Unsatisfiability Reasoning In ORM Conceptual Schemes. In Current Trends in Database Technology - EDBT 2006: Proceeding of the IFIP-2.6 International Conference on Semantics of a Networked. Pages ( ). LNCS 4254, Springer. Munich, Germany. ISBN: March [7] Mustafa Jarrar and Stijn Heymans: Towards Pattern-Based Reasoning For Friendly Ontology Debugging. Journal of Artificial Intelligence Tools. Volume 17. No.4. World Scientific Publishing. August [8] Mustafa Jarrar, Maria Keet, and Paolo Dongilli: Multilingual Verbalization Of ORM Conceptual Models And Axiomatized Ontologies. Technical report. STARLab, Vrije Universiteit Brussel, February [9] Sergey Lukichev and Mustafa Jarrar: Graphical Notations For Rule Modeling. Book chapter in "Handbook of Research on Emerging Rule-Based Languages and Technologies". IGI Global. ISBN: (2009) [10] Mustafa Jarrar: Modularization And Automatic Composition Of Object-Role Modeling (ORM) Schemes.OTM 2005 Workshops: Proceedings of the Object-Role Modeling (ORM'05). Pages ( ). LNCS 3762, Springer. ISBN: [11] Mustafa Jarrar: Towards Methodological Principles For Ontology Engineering. PhD Thesis. Vrije Universiteit Brussel. (May 2005) [12] Mustafa Jarrar, Jan Demey, and Robert Meersman: On Using Conceptual Data Modeling For Ontology Engineering. Journal on Data Semantics, Special issue on "Best papers from the ER/ODBASE/COOPIS 2002 Conferences". LNCS No 1. Springer [13] Jan Demey, Mustafa Jarrar, and Robert Meersman: A Markup Language For ORM Business Rules. Proceedings of the International Workshop on Rule Markup Languages for Business Rules on the Semantic Web (RuleML 2002). Pages( ). Volume 60. CEUR Workshop Proceedings. ISSN June 2002 [14] Mustafa Jarrar: Towards Effectiveness And Transparency In E-Business Transactions, An Ontology For Customer Complaint Management. A book chapter in "Semantic Web Methodologies for E-Business Applications". chapter 7. IGI Global. (2008) [15] Mustafa Jarrar: ORM Markup Language, Version 3. Technical Report. STAR Lab, Vrije Universiteit Brussel, Belgium. January